We've been in a very similar situation, also in the UK. A daughter who is strong for her size, brave, flexible, keen to learn and happiest when upside down, but who was rejected twice in trials for squads whose coaches said they were looking for exactly those qualities. It doesn't help that there seem to be far fewer options for kids here compared with in the US: either you're in the squad from an early age or you're stuck doing 45-60 mins a week with no hope of ever catching up with peers who are accelerating away doing 6, 8, 9 hours a week. So yeah it's very frustrating, especially as you can't know how much progress your child would make if they were getting more training.
My only suggestion would be to do something tremendously un-British and have a chat with your club. Find out how close she was at the last trial, if and when they'll be doing another one, whether the coaches think she might have a chance if she works on X, Y or Z. And yeah, have a look around at what other local clubs are up to, they might be looking for something different. There's no harm in sending her along for a trial just to see what happens.
The honesty and self-awareness of your post suggests you're worried about being seen as a pushy parent demanding that their child be fast-tracked to the Olympics because OBVIOUSLY she's a genius. But I learned very, very early in my gymnastics-parent journey that in the UK this is a sport where if you don't ask you don't get. If you sit and wait for someone to see the potential you see, it will likely never happen.
